Possible resources for you:
The Horry County Oral History Project supposedly has files online at: http://www.coastal.edu/library/hcohp.html
but I couldn't get the transcripts to come up....? You could email the site for help.
There's a book "Obituaries from Horry County newspapers, 1861-1914" that may list the Rabons. (21 libraries in the US have this book.)
Also, there are hundreds of other history books on Horry County. Try worldcat.org.
If a library near you does not have a book you want, they usually can get it through InterLibrary Loan from another library. Just ask your librarian.
You could also try contacting the cemetery to see if they have burial records that include cause of death.
Note: Even if you found that a disease was spreading in the area, that would not prove it caused these deaths. Their house could have burned down, for example.